Please submit a ticket with your issues here http://www.intel.com/support/mailform/maker/edisonwarrantyemail.htm . You will be contacted by an agent that will guide you through troubleshooting steps to help you.
OK - starting that now.
I think I have a similar issue with the J1 input side but I had not yet time to dig in a little bit deeper.
I noticed, that the board is getting very hot, especially the U15 - U4 ICs, what ever that is.
Did you see a similar behaviour?
No, I don’t see this behavior on my board. The area near U15 and U14 is not hot.
I had much the same issue: Edison w/ Arduino Expansion board no longer boot with 12V supply. Board get hot when connected to external 12V using J1 or Vin. I filled in RMA on warranty page and get replacement board.